R12 Release Notes

Chapter 21
GARCH Toolbox 1.0 Release Notes

Introduction to the GARCH Toolbox

The GARCH Toolbox was introduced in Release 11.1.

MATLAB and the GARCH Toolbox provide an integrated computing environment for modeling the volatility of univariate economic time series. The GARCH Toolbox uses a general ARMAX/GARCH composite model to perform simulation, forecasting, and parameter estimation of univariate time series in the presence of conditional heteroskedasticity. Supporting functions perform tasks such as pre- and post-estimation diagnostic testing, hypothesis testing of residuals, model order selection, and time series transformations. Graphics capabilities let you plot correlation functions and visually compare matched innovations, volatility, and return series.

GARCH modeling provides accurate forecasts of variances and covariances of asset returns through its ability to model time-varying conditional variances. As a consequence, you can apply GARCH models to such diverse fields as risk management, portfolio management and asset allocation, option pricing, foreign exchange, and the term structure of interest rates.

Using the GARCH Toolbox, you can:

• Perform Monte Carlo simulation of univariate returns, innovations, and conditional volatilities
• Specify conditional mean models of general ARMAX form and conditional models of general GARCH form for univariate asset returns
• Estimate parameters of general ARMAX/GARCH composite models via the maximum likelihood method
• Generate minimum mean square error forecasts of the conditional mean and conditional variance of univariate return series
• Perform pre- and post-estimation diagnostic and hypothesis testing, such as Engle's ARCH test, Ljung-Box Q-statistic test, likelihood ratio tests, and AIC/BIC model order selection
• Perform graphical correlation analysis, including auto-correlation, cross-correlation, and partial auto-correlation
• Convert price/return series to return/price series, and transform finite-order ARMA models to infinite-order AR and MA models

Known Software and Documentation Problems

Instrument Control Toolbox 1.0 Release Notes